Wednesday, February 21, 2007

Little is known about the ancient Chinese philosopher Huizi (or Hui Tzu, c. 300 BCE), but some of his paradoxes survive in the remoter chapters of the Zhuangzi. It's diverting to consider what reasoning might lie behind them. For example:

* I left for Yue today and arrived yesterday.* I know the center of the world: It is north of Yen [in the north] and south of Yue [in the south].* An egg has feathers.* Wheels never touch the ground.* No matter how swift the barbed arrow, there are times when it is neither moving nor at rest.* Take a pole one foot long, cut away half of it every day, and at the end of ten thousand generations there will still be some left.[Burton Watson, trans., except the first which is mine.]

Consider the first of these: I left for Yue today and arrived yesterday. Is there any way to make sense of it?

Well, the following are plausible principles:(a.) The last day you are in a locale is the day you left.(b.) The first day you are in a locale is the day you arrived.(c.) You are in a locale if at least 50% of your body is in that locale.

Now suppose I crossed over the border of Yue at exactly midnight, so that 50% of my body was in my home state at that instant and 50% was in Yue at that instant. It follows from (c) that:(d.) I was in my home state both yesterday and today.(e.) I was in Yue both yesterday and today.

By (a) and (d), I left for Yue today. However, by (b) and (e), I arrived yesterday.

Thanks for the comment, Warren! Your interpretation is completely possible. Seeing the whole body of paradoxes, though, it's striking how many of them plausibly involve space, time, the infinite, and the infinitesmal. Since that seems to be a general theme of Huizi's, I think that gives interpretations invoking that theme a little additional plausibility.

On the time zone issue, here's a thought. I don't know how the day was divided in ancient China, but if it had to do with sunrise or sunset, I can imagine seeing the sun set (transitioning to Thursday, say), then walking up a hill and seeing the sun again (thus going back to Wednesday). If I did this while crossing the border to Yue, I might have left for Yue today and arrived yesterday.

from my (admittedly limited) understanding of chinese/taoist philosophy, i think any attempt to "resolve" the paradox by means of conceptual argumentation is sort of missing the goal of the paradox in the first place.

that is, the taoist thought (and later chan [zen]) thought) is to use paradoxes like these to illustrate the LIMITS of conceptual thought. Conceptual thought is rooted in carving the world into dualistic categories like "yesterday" and "tomorrow", which we believe represent things in the world. however, we mistake these representations for the reality of the world itself, which is a mistake.

the function of the paradox is try to show us that when we use conceptual thought constructions to understand the world, we run into impossible situations.

the solution to the paradox is to directly realize their impossibility within a framework of conceptual thought.

when this happens, we realize that yesterday and tomorrow are in a sense the SAME thing, because one cannot exist without the other, and so on.

Good point, Steve! Something like that might be right if we interpret Huizi as a Daoist or quasi-Daoist. But should we interpret him that way? Zhuangzi is pretty critical of Huizi in the Inner Chapters. It doesn't seem that Zhuangzi, at least, sees Huizi as a Daoist.

But Daoist or non-Daoist, I grant that it is quite possible that Huizi thinks his paradoxes are irresolvable. However, even if that is the case, he needs something to motivate them, something to make it seem in some way plausible and not just stupid to say that I left today and arrived yesterday!

Very interesting stuff. And what a deft solution, Eric! Have you thought much about this "wheels never touch the ground" business? The "eggs have feathers" might trade on the ambiguity between "having feathers" in the manifest sense and having the propensity to grow feathers. But you never really know, given the dearth of textual evidence.

I really doubt that Huizi was a Daoist thinker, which is precisely why Zhuangzi so often picked him as a foil. But I can see why you might have read it this way, Steve, since (as Eric said) these paradoxes appear in a later chapter of the Zhuangzi.

Outside of the so-called "Inner Chapters" (= the first seven), the others are of very uncertain attribution. And there is even quite a bit of dispute about the attribution of the Inner Chapters, but that's a debate for the philologists...

I'm inclined to read the wheel never touching the ground as an issue about a circle forming a tangent to a line at only an infinitesmal (i.e., no measurable) point. The egg has feathers I'm inclined to think of as a sorites paradox.

These are very speculative of course, but it's cool how one can explain almost all the paradoxes by appeal to the infinite and infinitesmal (or insensibly small). (The traditional sorities paradox isn't a matter of insensibly small units, but it could be recast that way.)

Yes, I was thinking the same thing about the wheel paradox. I'm not sure about reading a sorites paradox into "eggs have feathers." But it's certainly plausible. This sounds like a good point at which to look up what A.C. Graham would have to say!

A.C. Graham -- in Disputers at least -- is pretty half-hearted, though he briefly suggests a few things, including something in the general direction of my leaving for Yue interpretation. Of course, there are many scattered discussions of these paradoxes in the secondary literature....

Here's my hypothesis: the bulk of Hui Shi's paradoxes are generated from Later Mohist assumptions about using boundaries to make spatiotemporal divisions. Hui Shi's point is that we should give up use of boundaries on pain of contradiction.

I have some preliminary blog notes trying to work out this hypothesis, over at:

http://www.whatisitliketobeablog.com/?p=16

and

http://www.whatisitliketobeablog.com/?p=18

And a more polished 12-page piece, for anyone who's interested. (e-mail bo_ram_lee at yahoo dot com).